Sunday, April 23, 2006 8:52 AM | rahel luethy | 5 comment(s)

reciprocity

compared to how much I love taking pictures, I know very little about the physics of photography. impressively little. I know that I like blurred backgrounds on portraits, thus I usually set the camera to aperture priority, choose a big aperture (i.e. one with a small number) and let the camera worry about exposure time. quite in contrast to my usual approach to almost anything (browsing/reading/discussing for hours) I never really worried about the meaning of these numbers. until a recent discussion about depth of field with olivier lead me to read a bit on wikipedia.

so here's a short recap of the quite cool system that some smart guys have come up with to facilitate life of photographers: as you probably know (unless you are even more oblivious than I am), the aperture number is a measure for the diameter of the entrance pupil. what I've just found out is that the numbers actually indicate fractions, namely, the ratio between the focal length and the diameter of the opening. for example, choosing f/16 with an 80 mm lens means that light is entering the camera body through a 5 mm hole.

theoretically, the opening can be changed gradually, so why the artificial f-numbers f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, etc.? this is a geometric progression, where each stop indicates another halving of the opening area (i.e. the diameter is multiplied by the square root of 2; numbers are rounded for convenience).

the smart thing is that shutter speeds (which determine exposure time) are arranged similarly. from wikipedia:

Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time, therefore to have the same exposure, you must have a shutter speed twice as fast (shutter open half as long)

even smarter, the film (read: chip) sensitivity is also arranged in simliar steps. thus changing any of these three (aperture, shutter speed, sensitivity) parameters can be compensated by stepping the other two up/down, respectively.

this fundamental law is called reciprocity.

8:19 AM |  nj said...

Is that how my phone's camera works too?

8:48 AM |  Anonymous said...

Früher musste man halt noch richtig überlegen, welche Belichtungszeit wohl die richtige war. Da gabs innen in den Filmverpackungen auch noch Angaben darüber, bei welchen Lichtverhältnissen welche Belichtungszeit/Blendenkombination zu verwenden ist.
Die Frage bleibt aber, weshalb die Schärfentiefe sich mit dem Öffnen der Blende verändert - und a)weshalb ich mit meiner Mittelformatkamera bei gleicher Brennweite und gleicher Blende ein kürzerer Schärfentiefenbereich habe und b)weshalb nach Angaben meiner Dir bekannten Mitarbeiter der Schärfentiefenbereich auf einem kleinen Kamerachip grundsätzlich immer grösser sei als auf einem Vollformatchip. Immerhin, es gibt eine Seite, wo Du Dir alles berechnen lassen kannst, aber was steckt da dahinter?

9:04 AM |  rahel luethy said...

1/ depth of field vs. aperture (link)

isn't a) and b) caused by the same effect? namely:

2/ depth of field vs. film format size (link)

9:18 AM |  rahel luethy said...

nj: yes, I think this is how your phone's camera works. however — unless you have a really fancy phone — the camera probably comes with a fixed focal length and just one (small) aperture. just like for a camera obscura, the depth of field is thus very large and there's no need to even adjust the focus. consequently, there aren't too many degrees of freedom for you to play around with ;-)

10:40 AM |  rahel luethy said...

oli: im footer deines verlinkten rechners hat's ein PDF, das die schaerfentiefe ausgezeichnet erklaert (link).